Name
STUDY LINK
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Date
Time
Unit 2: Family Letter
Estimation and Calculation
Computation is an important part of problem solving. Many of us were taught
that there is just one way to do each kind of computation. For example, we may
have learned to subtract by borrowing, without realizing that there are many
other methods of subtracting numbers.
In Unit 2, students will investigate several methods for adding, subtracting, and
multiplying whole numbers and decimals. Students will also take on an Estimation
Challenge in Unit 2. For this extended problem, they will measure classmates’
strides, and find a median length for all of them. Then they will use the median
length to estimate how far it would take to walk to various destinations.
Throughout the year, students will practice using estimation, calculators, as well as
mental and paper-and-pencil methods of computation. Students will identify which
method is most appropriate for solving a particular problem. From these exposures
to a variety of methods, they will learn that there are often several ways to
accomplish the same task and achieve the same result. Students are
encouraged to solve problems by whatever method they find most
comfortable.
Copyright © Wright Group/McGraw-Hill
Computation is usually not the first step in the problem-solving
process. One must first decide what numerical data are needed
to solve the problem and which operations need to be
performed. In this unit, your child will continue to develop
his or her problem-solving skills with a special focus on
writing and solving equations for problems.
Please keep this Family Letter for reference as your child works
through Unit 2.
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Unit 2: Family Letter cont.
Vocabulary
Important terms in Unit 2:
Estimation Challenge A problem for which it is
difficult, or even impossible, to find an exact answer.
Your child will make his or her best estimate and
then defend it.
partial-sums addition A method, or algorithm,
for adding in which sums are computed for each
place (ones, tens, hundreds, and so on) separately
and are then added to get a final answer.
magnitude estimate A rough estimate. A
magnitude estimate tells whether an answer should
be in the tens, hundreds, thousands, and so on.
1.
2.
3.
4.
Example: Give a magnitude estimate for 56 º 32
Step 1: Round 56 to 60.
Add
Add
Add
Add
100s
10s
1s
partial sums.
268
+ 483
600
140
+ 11
751
Partial-sums algorithm
Step 2: Round 32 to 30.
60 º 30 = 1,800, so a magnitude estimate
for 56 º 32 is in the thousands.
place value A number system that values a digit
number in a set of data.
according to its position in a number. In our number
system, each place has a value ten times that of
the place to its right and one-tenth the value of the
place to its left. For example, in the number 456, the
4 is in the hundreds place and has a value of 400.
mean The sum of a set of numbers divided by the
range The difference between the maximum and
number of numbers in the set. The mean is often
referred to simply as the average.
minimum in a set of data.
10s
100s
1,000s 10,000s
maximum The largest amount; the greatest
median The middle value in a set of data when
the data are listed in order from smallest to largest
or vice versa. If there is an even number of data
points, the median is the mean of the two middle
values.
number in a set of data.
trade-first subtraction A method, or algorithm,
for subtracting in which all trades are done before
any subtractions are carried out.
Example: 352 - 164
100s
3
- 1
10s
4
5/
6
Trade 1 ten for
10 ones.
1s
12
2/
4
100s
2
3/
-1
1
10s
14
4/
5/
6
8
1s
12
2/
4
8
Trade 1 hundred for 10 tens
and subtract in each column.
Copyright © Wright Group/McGraw-Hill
minimum The smallest amount; the smallest
reaction time The amount of time it takes a
person to react to something.
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Unit 2: Family Letter cont.
Building Skills through Games
In Unit 2, your child will practice computation skills
by playing these games. Detailed instructions are in
the Student Reference Book.
number cards 0–9, a six-sided die, and a calculator
to play this game. Multiplication Bull’s Eye provides
practice in estimating products.
Addition Top-It See Student Reference Book, page
333. This game for 2 to 4 players requires a
calculator and 4 each of the number cards 1–10,
and provides practice with place–value concepts
and methods of addition.
Number Top-It See Student Reference Book, page
326. Two to five players need 4 each of the
number cards 0–9 and a Place-Value Mat.
Students practice making large numbers.
High-Number Toss See Student Reference Book,
pages 320 and 321. Two players need one
six-sided die for this game. High-Number Toss helps
students review reading, writing, and comparing
decimals and large numbers.
Subtraction Target Practice See Student Reference
Book, page 331. One or more players need 4 each
of the number cards 0–9 and a calculator. In this
game, students review subtraction with multidigit
whole numbers and decimals.
Multiplication Bull’s-Eye See Student Reference
Book, page 323. Two players need 4 each of the
Do-Anytime Activities
To work with your child on the concepts taught in Units 1 and 2, try these activities:
Copyright © Wright Group/McGraw-Hill
1. When your child adds or subtracts multidigit numbers, talk about the strategy that works best.
Try not to impose the strategy that works best for you! Here are some problems to try:
467 + 343 = _______
________ = 761 + 79
894 - 444 = _______
842 - 59 = _______
2. As you encounter numbers while shopping or on license plates, ask your child to read the numbers
and identify digits in various places—thousands place, hundreds place, tens place, ones place, tenths
place, and hundredths place.
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Unit 2: Family Letter cont.
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As You Help Your Child with Homework
As your child brings assignments home, you might want to go over the instructions together, clarifying
them as necessary. The answers listed below will guide you through this unit’s Study Links.
Study Link 2 1
Study Link 2 5
Answers vary for Problems 1-5.
Answers vary for Problems 1–5.
6. 720
7. 90,361
8. 12
9. 18
Study Link 2 2
1. 571 and 261
2. 30, 20, and 7
3. 19 and 23
4. 533 and 125
5. 85.2 and 20.5, or 88.2 and 17.5; Because
the sum has a 7 in the tenths place, look
for numbers with tenths that add to 7:
85.2 + 20.5 = 105.7; and 88.2 + 17.5 = 105.7.
10. 47
7. 4.4
11. 208
8. 246
12. 3
9. 1.918
13. 8 R2
11. 6
8. 137
12. 84,018
9. 5.8
13. $453.98
15. 14
2. 30%: Unlikely
99%: Extremely likely
80%: Very likely
65%: Likely
5%: Extremely unlikely
20%: Very unlikely
35%: Unlikely
45%: 50-50 chance
Study Link 27
1. 1,000s; 70 ∗ 30 = 2,100
6. Sample answers: 45 ∗ 68 = 3,060;
684 ∗ 5 = 3,420; and 864 ∗ 5 = 4,320
Study Link 2 8
1. 152; 100s; 8 ∗ 20 = 160
Study Link 2 4
c. 148 + 127 = b
b. Total number of cards
3. 2,146; 1,000s; 40 ∗ 60 = 2,400
d. b = 275
4. 21; 10s; 5 ∗ 4 = 20.
e. 275 baseball cards
5. 26.04; 10s; 9 ∗ 3 = 27
2. a. 20.00; 3.89; 1.49 b. The amount of change
c. 20.00 - 3.89 - 1.49 = c,
or 20 - (3.89 + 1.49) = c
e. $14.62
3. a. 0.6; 1.15; 1.35; and 0.925
b. The length of the ribbons
c. b = 0.6 + 1.15 + 1.35 + 0.925
e. 4.025 meters
Study Link 2 9
1. 6,862; 1,000s
2. 88.8; 10s
3. 33.372; 10s
4. 100,224; 100,000s 5. 341.61; 100s
6. 9,989
7. 5 R2
8. 91
9. $19.00
Copyright © Wright Group/McGraw-Hill
2. 930; 100s; 150 ∗ 6 = 900
1. a. 148 and 127
d. b = 4.025
Very likely: 80%
Likely: 70%
5. 10s; 3 ∗ 4 = 12
5. 703 and 1,500
6. 25 and 9 7. 61
d. c = 14.62
1. Unlikely: 30%
Very unlikely: 15%
Extremely unlikely: 5%
4. 10s; 20 ∗ 2 = 40
3. Sample answer: 803 and 5,000
14. 98
9. 13
3. 10,000s; 100 ∗ 100 = 10,000
1. 451 and 299 2. 100.9 and 75.3
10. 18.85
8. 518
2. 1,000s; 10 ∗ 700 = 7,000
Study Link 2 3
4. 17 and 15
7. 29,616
Study Link 2 6
Sample answers:
6. 4,572
6. 5,622
Study Link 2 10
1. 390.756
2. 3,471.549
3. 9,340
4. 244
5. 44,604
6. 19 R2
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